Question: Simplify the following expression and state the condition under which the simplification is valid. $y = \dfrac{7n^2 - 7n - 210}{2n^2 + 12n + 10}$
Explanation: First factor out the greatest common factors in the numerator and in the denominator. $ y = \dfrac {7(n^2 - n - 30)} {2(n^2 + 6n + 5)} $ $ y = \dfrac{7}{2} \cdot \dfrac{n^2 - n - 30}{n^2 + 6n + 5} $ Next factor the numerator and denominator. $ y = \dfrac{7}{2} \cdot \dfrac{(n + 5)(n - 6)}{(n + 5)(n + 1)}$ Assuming $n \neq -5$ , we can cancel the $n + 5$ $ y = \dfrac{7}{2} \cdot \dfrac{n - 6}{n + 1}$ Therefore: $ y = \dfrac{ 7(n - 6)}{ 2(n + 1)}$, $n \neq -5$